Safe Haskell	Safe
Language	Haskell2010

Control.Monad.Trans.Free.Ap

Contents

The base functor
The free monad transformer
The free monad
Operations
Operations of free monad
Free Monads With Class

Description

Given an applicative, the free monad transformer.

Synopsis

data FreeF (f :: Type -> Type) a b
- = Pure a
- | Free (f b)
newtype FreeT (f :: Type -> Type) (m :: Type -> Type) a = FreeT {
- runFreeT :: m (FreeF f a (FreeT f m a))
}
type Free (f :: Type -> Type) = FreeT f Identity
free :: forall (f :: Type -> Type) a. FreeF f a (Free f a) -> Free f a
runFree :: forall (f :: Type -> Type) a. Free f a -> FreeF f a (Free f a)
liftF :: (Functor f, MonadFree f m) => f a -> m a
iterT :: (Applicative f, Monad m) => (f (m a) -> m a) -> FreeT f m a -> m a
iterTM :: forall f (m :: Type -> Type) t a. (Applicative f, Monad m, MonadTrans t, Monad (t m)) => (f (t m a) -> t m a) -> FreeT f m a -> t m a
hoistFreeT :: forall m (f :: Type -> Type) n b. (Functor m, Applicative f) => (forall a. m a -> n a) -> FreeT f m b -> FreeT f n b
transFreeT :: forall (m :: Type -> Type) g f b. (Monad m, Applicative g) => (forall a. f a -> g a) -> FreeT f m b -> FreeT g m b
joinFreeT :: forall m (f :: Type -> Type) a. (Monad m, Traversable f, Applicative f) => FreeT f m a -> m (Free f a)
cutoff :: forall (f :: Type -> Type) (m :: Type -> Type) a. (Applicative f, Monad m) => Integer -> FreeT f m a -> FreeT f m (Maybe a)
partialIterT :: Monad m => Integer -> (forall a. f a -> m a) -> FreeT f m b -> FreeT f m b
intersperseT :: forall (m :: Type -> Type) f a b. (Monad m, Applicative f) => f a -> FreeT f m b -> FreeT f m b
intercalateT :: forall (m :: Type -> Type) t a b. (Monad m, MonadTrans t, Monad (t m)) => t m a -> FreeT (t m) m b -> t m b
retractT :: forall t (m :: Type -> Type) a. (MonadTrans t, Monad (t m), Monad m) => FreeT (t m) m a -> t m a
retract :: Monad f => Free f a -> f a
iter :: Applicative f => (f a -> a) -> Free f a -> a
iterM :: (Applicative f, Monad m) => (f (m a) -> m a) -> Free f a -> m a
class Monad m => MonadFree (f :: Type -> Type) (m :: Type -> Type) | m -> f where
- wrap :: f (m a) -> m a

The base functor

data FreeF (f :: Type -> Type) a b Source #

The base functor for a free monad.

Constructors

Pure a
Free (f b)

Instances

Instances details

Generic1 (FreeF f a :: Type -> Type) Source #

Instance details

Defined in Control.Monad.Trans.Free.Ap

Associated Types

type Rep1 (FreeF f a :: Type -> Type)

Instance details

Defined in Control.Monad.Trans.Free.Ap

type Rep1 (FreeF f a :: Type -> Type) = D1 ('MetaData "FreeF" "Control.Monad.Trans.Free.Ap" "free-5.2-LmzEdwCIXEmChsYc63CoVW" 'False) (C1 ('MetaCons "Pure" 'PrefixI 'False) (S1 ('MetaSel ('Nothing :: Maybe Symbol) 'NoSourceUnpackedness 'NoSourceStrictness 'DecidedLazy) (Rec0 a)) :+: C1 ('MetaCons "Free" 'PrefixI 'False) (S1 ('MetaSel ('Nothing :: Maybe Symbol) 'NoSourceUnpackedness 'NoSourceStrictness 'DecidedLazy) (Rec1 f)))

Methods

from1 :: FreeF f a a0 -> Rep1 (FreeF f a) a0 #

to1 :: Rep1 (FreeF f a) a0 -> FreeF f a a0 #

Foldable f => Bifoldable (FreeF f) Source #

Instance details

Defined in Control.Monad.Trans.Free.Ap

Methods

bifold :: Monoid m => FreeF f m m -> m #

bifoldMap :: Monoid m => (a -> m) -> (b -> m) -> FreeF f a b -> m #

bifoldr :: (a -> c -> c) -> (b -> c -> c) -> c -> FreeF f a b -> c #

bifoldl :: (c -> a -> c) -> (c -> b -> c) -> c -> FreeF f a b -> c #

Functor f => Bifunctor (FreeF f) Source #

Instance details

Defined in Control.Monad.Trans.Free.Ap

Methods

bimap :: (a -> b) -> (c -> d) -> FreeF f a c -> FreeF f b d #

first :: (a -> b) -> FreeF f a c -> FreeF f b c #

second :: (b -> c) -> FreeF f a b -> FreeF f a c #

Traversable f => Bitraversable (FreeF f) Source #

Instance details

Defined in Control.Monad.Trans.Free.Ap

Methods

bitraverse :: Applicative f0 => (a -> f0 c) -> (b -> f0 d) -> FreeF f a b -> f0 (FreeF f c d) #

Eq1 f => Eq2 (FreeF f) Source #

Instance details

Defined in Control.Monad.Trans.Free.Ap

Methods

liftEq2 :: (a -> b -> Bool) -> (c -> d -> Bool) -> FreeF f a c -> FreeF f b d -> Bool #

Ord1 f => Ord2 (FreeF f) Source #

Instance details

Defined in Control.Monad.Trans.Free.Ap

Methods

liftCompare2 :: (a -> b -> Ordering) -> (c -> d -> Ordering) -> FreeF f a c -> FreeF f b d -> Ordering #

Read1 f => Read2 (FreeF f) Source #

Instance details

Defined in Control.Monad.Trans.Free.Ap

Methods

liftReadsPrec2 :: (Int -> ReadS a) -> ReadS [a] -> (Int -> ReadS b) -> ReadS [b] -> Int -> ReadS (FreeF f a b) #

liftReadList2 :: (Int -> ReadS a) -> ReadS [a] -> (Int -> ReadS b) -> ReadS [b] -> ReadS [FreeF f a b] #

liftReadPrec2 :: ReadPrec a -> ReadPrec [a] -> ReadPrec b -> ReadPrec [b] -> ReadPrec (FreeF f a b) #

liftReadListPrec2 :: ReadPrec a -> ReadPrec [a] -> ReadPrec b -> ReadPrec [b] -> ReadPrec [FreeF f a b] #

Show1 f => Show2 (FreeF f) Source #

Instance details

Defined in Control.Monad.Trans.Free.Ap

Methods

liftShowsPrec2 :: (Int -> a -> ShowS) -> ([a] -> ShowS) -> (Int -> b -> ShowS) -> ([b] -> ShowS) -> Int -> FreeF f a b -> ShowS #

liftShowList2 :: (Int -> a -> ShowS) -> ([a] -> ShowS) -> (Int -> b -> ShowS) -> ([b] -> ShowS) -> [FreeF f a b] -> ShowS #

Foldable f => Foldable (FreeF f a) Source #

Instance details

Defined in Control.Monad.Trans.Free.Ap

Methods

fold :: Monoid m => FreeF f a m -> m #

foldMap :: Monoid m => (a0 -> m) -> FreeF f a a0 -> m #

foldMap' :: Monoid m => (a0 -> m) -> FreeF f a a0 -> m #

foldr :: (a0 -> b -> b) -> b -> FreeF f a a0 -> b #

foldr' :: (a0 -> b -> b) -> b -> FreeF f a a0 -> b #

foldl :: (b -> a0 -> b) -> b -> FreeF f a a0 -> b #

foldl' :: (b -> a0 -> b) -> b -> FreeF f a a0 -> b #

foldr1 :: (a0 -> a0 -> a0) -> FreeF f a a0 -> a0 #

foldl1 :: (a0 -> a0 -> a0) -> FreeF f a a0 -> a0 #

toList :: FreeF f a a0 -> [a0] #

null :: FreeF f a a0 -> Bool #

length :: FreeF f a a0 -> Int #

elem :: Eq a0 => a0 -> FreeF f a a0 -> Bool #

maximum :: Ord a0 => FreeF f a a0 -> a0 #

minimum :: Ord a0 => FreeF f a a0 -> a0 #

sum :: Num a0 => FreeF f a a0 -> a0 #

product :: Num a0 => FreeF f a a0 -> a0 #

(Eq1 f, Eq a) => Eq1 (FreeF f a) Source #

Instance details

Defined in Control.Monad.Trans.Free.Ap

Methods

liftEq :: (a0 -> b -> Bool) -> FreeF f a a0 -> FreeF f a b -> Bool #

(Ord1 f, Ord a) => Ord1 (FreeF f a) Source #

Instance details

Defined in Control.Monad.Trans.Free.Ap

Methods

liftCompare :: (a0 -> b -> Ordering) -> FreeF f a a0 -> FreeF f a b -> Ordering #

(Read1 f, Read a) => Read1 (FreeF f a) Source #

Instance details

Defined in Control.Monad.Trans.Free.Ap

Methods

liftReadsPrec :: (Int -> ReadS a0) -> ReadS [a0] -> Int -> ReadS (FreeF f a a0) #

liftReadList :: (Int -> ReadS a0) -> ReadS [a0] -> ReadS [FreeF f a a0] #

liftReadPrec :: ReadPrec a0 -> ReadPrec [a0] -> ReadPrec (FreeF f a a0) #

liftReadListPrec :: ReadPrec a0 -> ReadPrec [a0] -> ReadPrec [FreeF f a a0] #

(Show1 f, Show a) => Show1 (FreeF f a) Source #

Instance details

Defined in Control.Monad.Trans.Free.Ap

Methods

liftShowsPrec :: (Int -> a0 -> ShowS) -> ([a0] -> ShowS) -> Int -> FreeF f a a0 -> ShowS #

liftShowList :: (Int -> a0 -> ShowS) -> ([a0] -> ShowS) -> [FreeF f a a0] -> ShowS #

Traversable f => Traversable (FreeF f a) Source #

Instance details

Defined in Control.Monad.Trans.Free.Ap

Methods

traverse :: Applicative f0 => (a0 -> f0 b) -> FreeF f a a0 -> f0 (FreeF f a b) #

sequenceA :: Applicative f0 => FreeF f a (f0 a0) -> f0 (FreeF f a a0) #

mapM :: Monad m => (a0 -> m b) -> FreeF f a a0 -> m (FreeF f a b) #

sequence :: Monad m => FreeF f a (m a0) -> m (FreeF f a a0) #

Functor f => Functor (FreeF f a) Source #

Instance details

Defined in Control.Monad.Trans.Free.Ap

Methods

fmap :: (a0 -> b) -> FreeF f a a0 -> FreeF f a b #

(<$) :: a0 -> FreeF f a b -> FreeF f a a0 #

(Typeable f, Typeable b, Data a, Data (f b)) => Data (FreeF f a b) Source #

Instance details

Defined in Control.Monad.Trans.Free.Ap

Methods

gfoldl :: (forall d b0. Data d => c (d -> b0) -> d -> c b0) -> (forall g. g -> c g) -> FreeF f a b -> c (FreeF f a b) #

gunfold :: (forall b0 r. Data b0 => c (b0 -> r) -> c r) -> (forall r. r -> c r) -> Constr -> c (FreeF f a b) #

toConstr :: FreeF f a b -> Constr #

dataTypeOf :: FreeF f a b -> DataType #

dataCast1 :: Typeable t => (forall d. Data d => c (t d)) -> Maybe (c (FreeF f a b)) #

dataCast2 :: Typeable t => (forall d e. (Data d, Data e) => c (t d e)) -> Maybe (c (FreeF f a b)) #

gmapT :: (forall b0. Data b0 => b0 -> b0) -> FreeF f a b -> FreeF f a b #

gmapQl :: (r -> r' -> r) -> r -> (forall d. Data d => d -> r') -> FreeF f a b -> r #

gmapQr :: forall r r'. (r' -> r -> r) -> r -> (forall d. Data d => d -> r') -> FreeF f a b -> r #

gmapQ :: (forall d. Data d => d -> u) -> FreeF f a b -> [u] #

gmapQi :: Int -> (forall d. Data d => d -> u) -> FreeF f a b -> u #

gmapM :: Monad m => (forall d. Data d => d -> m d) -> FreeF f a b -> m (FreeF f a b) #

gmapMp :: MonadPlus m => (forall d. Data d => d -> m d) -> FreeF f a b -> m (FreeF f a b) #

gmapMo :: MonadPlus m => (forall d. Data d => d -> m d) -> FreeF f a b -> m (FreeF f a b) #

Generic (FreeF f a b) Source #

Instance details

Defined in Control.Monad.Trans.Free.Ap

Associated Types

type Rep (FreeF f a b)

Instance details

Defined in Control.Monad.Trans.Free.Ap

type Rep (FreeF f a b) = D1 ('MetaData "FreeF" "Control.Monad.Trans.Free.Ap" "free-5.2-LmzEdwCIXEmChsYc63CoVW" 'False) (C1 ('MetaCons "Pure" 'PrefixI 'False) (S1 ('MetaSel ('Nothing :: Maybe Symbol) 'NoSourceUnpackedness 'NoSourceStrictness 'DecidedLazy) (Rec0 a)) :+: C1 ('MetaCons "Free" 'PrefixI 'False) (S1 ('MetaSel ('Nothing :: Maybe Symbol) 'NoSourceUnpackedness 'NoSourceStrictness 'DecidedLazy) (Rec0 (f b))))

Methods

from :: FreeF f a b -> Rep (FreeF f a b) x #

to :: Rep (FreeF f a b) x -> FreeF f a b #

(Read a, Read (f b)) => Read (FreeF f a b) Source #

Instance details

Defined in Control.Monad.Trans.Free.Ap

Methods

readsPrec :: Int -> ReadS (FreeF f a b) #

readList :: ReadS [FreeF f a b] #

readPrec :: ReadPrec (FreeF f a b) #

readListPrec :: ReadPrec [FreeF f a b] #

(Show a, Show (f b)) => Show (FreeF f a b) Source #

Instance details

Defined in Control.Monad.Trans.Free.Ap

Methods

showsPrec :: Int -> FreeF f a b -> ShowS #

show :: FreeF f a b -> String #

showList :: [FreeF f a b] -> ShowS #

(Eq a, Eq (f b)) => Eq (FreeF f a b) Source #

Instance details

Defined in Control.Monad.Trans.Free.Ap

Methods

(==) :: FreeF f a b -> FreeF f a b -> Bool #

(/=) :: FreeF f a b -> FreeF f a b -> Bool #

(Ord a, Ord (f b)) => Ord (FreeF f a b) Source #

Instance details

Defined in Control.Monad.Trans.Free.Ap

Methods

compare :: FreeF f a b -> FreeF f a b -> Ordering #

(<) :: FreeF f a b -> FreeF f a b -> Bool #

(<=) :: FreeF f a b -> FreeF f a b -> Bool #

(>) :: FreeF f a b -> FreeF f a b -> Bool #

(>=) :: FreeF f a b -> FreeF f a b -> Bool #

max :: FreeF f a b -> FreeF f a b -> FreeF f a b #

min :: FreeF f a b -> FreeF f a b -> FreeF f a b #

type Rep1 (FreeF f a :: Type -> Type) Source #

Instance details

Defined in Control.Monad.Trans.Free.Ap

type Rep1 (FreeF f a :: Type -> Type) = D1 ('MetaData "FreeF" "Control.Monad.Trans.Free.Ap" "free-5.2-LmzEdwCIXEmChsYc63CoVW" 'False) (C1 ('MetaCons "Pure" 'PrefixI 'False) (S1 ('MetaSel ('Nothing :: Maybe Symbol) 'NoSourceUnpackedness 'NoSourceStrictness 'DecidedLazy) (Rec0 a)) :+: C1 ('MetaCons "Free" 'PrefixI 'False) (S1 ('MetaSel ('Nothing :: Maybe Symbol) 'NoSourceUnpackedness 'NoSourceStrictness 'DecidedLazy) (Rec1 f)))

type Rep (FreeF f a b) Source #

Instance details

Defined in Control.Monad.Trans.Free.Ap

type Rep (FreeF f a b) = D1 ('MetaData "FreeF" "Control.Monad.Trans.Free.Ap" "free-5.2-LmzEdwCIXEmChsYc63CoVW" 'False) (C1 ('MetaCons "Pure" 'PrefixI 'False) (S1 ('MetaSel ('Nothing :: Maybe Symbol) 'NoSourceUnpackedness 'NoSourceStrictness 'DecidedLazy) (Rec0 a)) :+: C1 ('MetaCons "Free" 'PrefixI 'False) (S1 ('MetaSel ('Nothing :: Maybe Symbol) 'NoSourceUnpackedness 'NoSourceStrictness 'DecidedLazy) (Rec0 (f b))))

The free monad transformer

newtype FreeT (f :: Type -> Type) (m :: Type -> Type) a Source #

The "free monad transformer" for an applicative f

Constructors

FreeT
Fields runFreeT :: m (FreeF f a (FreeT f m a))

Instances

Instances details

(Applicative f, Monad m) => MonadFree f (FreeT f m) Source #
Instance details Defined in Control.Monad.Trans.Free.Ap Methods wrap :: f (FreeT f m a) -> FreeT f m a Source #
(Applicative f, MonadError e m) => MonadError e (FreeT f m) Source #
Instance details Defined in Control.Monad.Trans.Free.Ap Methods throwError :: e -> FreeT f m a # catchError :: FreeT f m a -> (e -> FreeT f m a) -> FreeT f m a #
(Applicative f, MonadReader r m) => MonadReader r (FreeT f m) Source #
Instance details Defined in Control.Monad.Trans.Free.Ap Methods ask :: FreeT f m r # local :: (r -> r) -> FreeT f m a -> FreeT f m a # reader :: (r -> a) -> FreeT f m a #
(Applicative f, MonadState s m) => MonadState s (FreeT f m) Source #
Instance details Defined in Control.Monad.Trans.Free.Ap Methods get :: FreeT f m s # put :: s -> FreeT f m () # state :: (s -> (a, s)) -> FreeT f m a #
(Applicative f, MonadWriter w m) => MonadWriter w (FreeT f m) Source #
Instance details Defined in Control.Monad.Trans.Free.Ap Methods writer :: (a, w) -> FreeT f m a # tell :: w -> FreeT f m () # listen :: FreeT f m a -> FreeT f m (a, w) # pass :: FreeT f m (a, w -> w) -> FreeT f m a #
Applicative f => MonadTrans (FreeT f) Source #
Instance details Defined in Control.Monad.Trans.Free.Ap Methods lift :: Monad m => m a -> FreeT f m a #
(Applicative f, MonadFail m) => MonadFail (FreeT f m) Source #
Instance details Defined in Control.Monad.Trans.Free.Ap Methods fail :: String -> FreeT f m a #
(Applicative f, MonadIO m) => MonadIO (FreeT f m) Source #
Instance details Defined in Control.Monad.Trans.Free.Ap Methods liftIO :: IO a -> FreeT f m a #
(Foldable m, Foldable f) => Foldable (FreeT f m) Source #
Instance details Defined in Control.Monad.Trans.Free.Ap Methods fold :: Monoid m0 => FreeT f m m0 -> m0 # foldMap :: Monoid m0 => (a -> m0) -> FreeT f m a -> m0 # foldMap' :: Monoid m0 => (a -> m0) -> FreeT f m a -> m0 # foldr :: (a -> b -> b) -> b -> FreeT f m a -> b # foldr' :: (a -> b -> b) -> b -> FreeT f m a -> b # foldl :: (b -> a -> b) -> b -> FreeT f m a -> b # foldl' :: (b -> a -> b) -> b -> FreeT f m a -> b # foldr1 :: (a -> a -> a) -> FreeT f m a -> a # foldl1 :: (a -> a -> a) -> FreeT f m a -> a # toList :: FreeT f m a -> [a] # null :: FreeT f m a -> Bool # length :: FreeT f m a -> Int # elem :: Eq a => a -> FreeT f m a -> Bool # maximum :: Ord a => FreeT f m a -> a # minimum :: Ord a => FreeT f m a -> a # sum :: Num a => FreeT f m a -> a # product :: Num a => FreeT f m a -> a #
(Eq1 f, Eq1 m) => Eq1 (FreeT f m) Source #
Instance details Defined in Control.Monad.Trans.Free.Ap Methods liftEq :: (a -> b -> Bool) -> FreeT f m a -> FreeT f m b -> Bool #
(Ord1 f, Ord1 m) => Ord1 (FreeT f m) Source #
Instance details Defined in Control.Monad.Trans.Free.Ap Methods liftCompare :: (a -> b -> Ordering) -> FreeT f m a -> FreeT f m b -> Ordering #
(Read1 f, Read1 m) => Read1 (FreeT f m) Source #
Instance details Defined in Control.Monad.Trans.Free.Ap Methods liftReadsPrec :: (Int -> ReadS a) -> ReadS [a] -> Int -> ReadS (FreeT f m a) # liftReadList :: (Int -> ReadS a) -> ReadS [a] -> ReadS [FreeT f m a] # liftReadPrec :: ReadPrec a -> ReadPrec [a] -> ReadPrec (FreeT f m a) # liftReadListPrec :: ReadPrec a -> ReadPrec [a] -> ReadPrec [FreeT f m a] #
(Show1 f, Show1 m) => Show1 (FreeT f m) Source #
Instance details Defined in Control.Monad.Trans.Free.Ap Methods liftShowsPrec :: (Int -> a -> ShowS) -> ([a] -> ShowS) -> Int -> FreeT f m a -> ShowS # liftShowList :: (Int -> a -> ShowS) -> ([a] -> ShowS) -> [FreeT f m a] -> ShowS #
(Monad m, Traversable m, Traversable f) => Traversable (FreeT f m) Source #
Instance details Defined in Control.Monad.Trans.Free.Ap Methods traverse :: Applicative f0 => (a -> f0 b) -> FreeT f m a -> f0 (FreeT f m b) # sequenceA :: Applicative f0 => FreeT f m (f0 a) -> f0 (FreeT f m a) # mapM :: Monad m0 => (a -> m0 b) -> FreeT f m a -> m0 (FreeT f m b) # sequence :: Monad m0 => FreeT f m (m0 a) -> m0 (FreeT f m a) #
(Applicative f, MonadPlus m) => Alternative (FreeT f m) Source #
Instance details Defined in Control.Monad.Trans.Free.Ap Methods empty :: FreeT f m a # (<\|>) :: FreeT f m a -> FreeT f m a -> FreeT f m a # some :: FreeT f m a -> FreeT f m [a] # many :: FreeT f m a -> FreeT f m [a] #
(Applicative f, Applicative m) => Applicative (FreeT f m) Source #
Instance details Defined in Control.Monad.Trans.Free.Ap Methods pure :: a -> FreeT f m a # (<>) :: FreeT f m (a -> b) -> FreeT f m a -> FreeT f m b # liftA2 :: (a -> b -> c) -> FreeT f m a -> FreeT f m b -> FreeT f m c # (>) :: FreeT f m a -> FreeT f m b -> FreeT f m b # (<*) :: FreeT f m a -> FreeT f m b -> FreeT f m a #
(Functor f, Functor m) => Functor (FreeT f m) Source #
Instance details Defined in Control.Monad.Trans.Free.Ap Methods fmap :: (a -> b) -> FreeT f m a -> FreeT f m b # (<$) :: a -> FreeT f m b -> FreeT f m a #
(Applicative f, Monad m) => Monad (FreeT f m) Source #
Instance details Defined in Control.Monad.Trans.Free.Ap Methods (>>=) :: FreeT f m a -> (a -> FreeT f m b) -> FreeT f m b # (>>) :: FreeT f m a -> FreeT f m b -> FreeT f m b # return :: a -> FreeT f m a #
(Applicative f, MonadPlus m) => MonadPlus (FreeT f m) Source #
Instance details Defined in Control.Monad.Trans.Free.Ap Methods mzero :: FreeT f m a # mplus :: FreeT f m a -> FreeT f m a -> FreeT f m a #
(Applicative f, MonadCatch m) => MonadCatch (FreeT f m) Source #
Instance details Defined in Control.Monad.Trans.Free.Ap Methods catch :: (HasCallStack, Exception e) => FreeT f m a -> (e -> FreeT f m a) -> FreeT f m a #
(Applicative f, MonadThrow m) => MonadThrow (FreeT f m) Source #
Instance details Defined in Control.Monad.Trans.Free.Ap Methods throwM :: (HasCallStack, Exception e) => e -> FreeT f m a #
(Applicative f, MonadCont m) => MonadCont (FreeT f m) Source #
Instance details Defined in Control.Monad.Trans.Free.Ap Methods callCC :: ((a -> FreeT f m b) -> FreeT f m a) -> FreeT f m a #
(Apply f, Apply m) => Apply (FreeT f m) Source #
Instance details Defined in Control.Monad.Trans.Free.Ap Methods (<.>) :: FreeT f m (a -> b) -> FreeT f m a -> FreeT f m b # (.>) :: FreeT f m a -> FreeT f m b -> FreeT f m b # (<.) :: FreeT f m a -> FreeT f m b -> FreeT f m a # liftF2 :: (a -> b -> c) -> FreeT f m a -> FreeT f m b -> FreeT f m c #
(Apply f, Apply m, Monad m) => Bind (FreeT f m) Source #
Instance details Defined in Control.Monad.Trans.Free.Ap Methods (>>-) :: FreeT f m a -> (a -> FreeT f m b) -> FreeT f m b # join :: FreeT f m (FreeT f m a) -> FreeT f m a #
(Typeable f, Typeable m, Data (m (FreeF f a (FreeT f m a))), Data a) => Data (FreeT f m a) Source #
Instance details Defined in Control.Monad.Trans.Free.Ap Methods gfoldl :: (forall d b. Data d => c (d -> b) -> d -> c b) -> (forall g. g -> c g) -> FreeT f m a -> c (FreeT f m a) # gunfold :: (forall b r. Data b => c (b -> r) -> c r) -> (forall r. r -> c r) -> Constr -> c (FreeT f m a) # toConstr :: FreeT f m a -> Constr # dataTypeOf :: FreeT f m a -> DataType # dataCast1 :: Typeable t => (forall d. Data d => c (t d)) -> Maybe (c (FreeT f m a)) # dataCast2 :: Typeable t => (forall d e. (Data d, Data e) => c (t d e)) -> Maybe (c (FreeT f m a)) # gmapT :: (forall b. Data b => b -> b) -> FreeT f m a -> FreeT f m a # gmapQl :: (r -> r' -> r) -> r -> (forall d. Data d => d -> r') -> FreeT f m a -> r # gmapQr :: forall r r'. (r' -> r -> r) -> r -> (forall d. Data d => d -> r') -> FreeT f m a -> r # gmapQ :: (forall d. Data d => d -> u) -> FreeT f m a -> [u] # gmapQi :: Int -> (forall d. Data d => d -> u) -> FreeT f m a -> u # gmapM :: Monad m0 => (forall d. Data d => d -> m0 d) -> FreeT f m a -> m0 (FreeT f m a) # gmapMp :: MonadPlus m0 => (forall d. Data d => d -> m0 d) -> FreeT f m a -> m0 (FreeT f m a) # gmapMo :: MonadPlus m0 => (forall d. Data d => d -> m0 d) -> FreeT f m a -> m0 (FreeT f m a) #
(Read1 f, Read1 m, Read a) => Read (FreeT f m a) Source #
Instance details Defined in Control.Monad.Trans.Free.Ap Methods readsPrec :: Int -> ReadS (FreeT f m a) # readList :: ReadS [FreeT f m a] # readPrec :: ReadPrec (FreeT f m a) # readListPrec :: ReadPrec [FreeT f m a] #
(Show1 f, Show1 m, Show a) => Show (FreeT f m a) Source #
Instance details Defined in Control.Monad.Trans.Free.Ap Methods showsPrec :: Int -> FreeT f m a -> ShowS # show :: FreeT f m a -> String # showList :: [FreeT f m a] -> ShowS #
(Eq1 f, Eq1 m, Eq a) => Eq (FreeT f m a) Source #
Instance details Defined in Control.Monad.Trans.Free.Ap Methods (==) :: FreeT f m a -> FreeT f m a -> Bool # (/=) :: FreeT f m a -> FreeT f m a -> Bool #
(Ord1 f, Ord1 m, Ord a) => Ord (FreeT f m a) Source #
Instance details Defined in Control.Monad.Trans.Free.Ap Methods compare :: FreeT f m a -> FreeT f m a -> Ordering # (<) :: FreeT f m a -> FreeT f m a -> Bool # (<=) :: FreeT f m a -> FreeT f m a -> Bool # (>) :: FreeT f m a -> FreeT f m a -> Bool # (>=) :: FreeT f m a -> FreeT f m a -> Bool # max :: FreeT f m a -> FreeT f m a -> FreeT f m a # min :: FreeT f m a -> FreeT f m a -> FreeT f m a #

The free monad

type Free (f :: Type -> Type) = FreeT f Identity Source #

The "free monad" for an applicative f.

free :: forall (f :: Type -> Type) a. FreeF f a (Free f a) -> Free f a Source #

Pushes a layer into a free monad value.

runFree :: forall (f :: Type -> Type) a. Free f a -> FreeF f a (Free f a) Source #

Evaluates the first layer out of a free monad value.

Operations

liftF :: (Functor f, MonadFree f m) => f a -> m a Source #

A version of lift that can be used with just a Functor for f.

iterT :: (Applicative f, Monad m) => (f (m a) -> m a) -> FreeT f m a -> m a Source #

Given an applicative homomorphism from f (m a) to m a, tear down a free monad transformer using iteration.

iterTM :: forall f (m :: Type -> Type) t a. (Applicative f, Monad m, MonadTrans t, Monad (t m)) => (f (t m a) -> t m a) -> FreeT f m a -> t m a Source #

Given an applicative homomorphism from f (t m a) to t m a, tear down a free monad transformer using iteration over a transformer.

hoistFreeT :: forall m (f :: Type -> Type) n b. (Functor m, Applicative f) => (forall a. m a -> n a) -> FreeT f m b -> FreeT f n b Source #

Lift a monad homomorphism from m to n into a monad homomorphism from FreeT f m to FreeT f n

hoistFreeT :: (Functor m, Applicative f) => (m ~> n) -> FreeT f m ~> FreeT f n

transFreeT :: forall (m :: Type -> Type) g f b. (Monad m, Applicative g) => (forall a. f a -> g a) -> FreeT f m b -> FreeT g m b Source #

Lift an applicative homomorphism from f to g into a monad homomorphism from FreeT f m to FreeT g m

joinFreeT :: forall m (f :: Type -> Type) a. (Monad m, Traversable f, Applicative f) => FreeT f m a -> m (Free f a) Source #

Pull out and join m layers of FreeT f m a.

cutoff :: forall (f :: Type -> Type) (m :: Type -> Type) a. (Applicative f, Monad m) => Integer -> FreeT f m a -> FreeT f m (Maybe a) Source #

Cuts off a tree of computations at a given depth. If the depth is 0 or less, no computation nor monadic effects will take place.

Some examples (n ≥ 0):

cutoff 0     _        ≡ return Nothing
cutoff (n+1) . return ≡ return . Just
cutoff (n+1) . lift   ≡ lift . liftM Just
cutoff (n+1) . wrap   ≡ wrap . fmap (cutoff n)

Calling retract . cutoff n is always terminating, provided each of the steps in the iteration is terminating.

partialIterT :: Monad m => Integer -> (forall a. f a -> m a) -> FreeT f m b -> FreeT f m b Source #

partialIterT n phi m interprets first n layers of m using phi. This is sort of the opposite for cutoff.

Some examples (n ≥ 0):

partialIterT 0 _ m              ≡ m
partialIterT (n+1) phi . return ≡ return
partialIterT (n+1) phi . lift   ≡ lift
partialIterT (n+1) phi . wrap   ≡ join . lift . phi

intersperseT :: forall (m :: Type -> Type) f a b. (Monad m, Applicative f) => f a -> FreeT f m b -> FreeT f m b Source #

intersperseT f m inserts a layer f between every two layers in m.

intersperseT f . return ≡ return
intersperseT f . lift   ≡ lift
intersperseT f . wrap   ≡ wrap . fmap (iterTM (wrap . (<$ f) . wrap))

intercalateT :: forall (m :: Type -> Type) t a b. (Monad m, MonadTrans t, Monad (t m)) => t m a -> FreeT (t m) m b -> t m b Source #

intercalateT f m inserts a layer f between every two layers in m and then retracts the result.

intercalateT f ≡ retractT . intersperseT f

retractT :: forall t (m :: Type -> Type) a. (MonadTrans t, Monad (t m), Monad m) => FreeT (t m) m a -> t m a Source #

Tear down a free monad transformer using Monad instance for t m.

Operations of free monad

retract :: Monad f => Free f a -> f a Source #

retract is the left inverse of liftF

retract . liftF = id

iter :: Applicative f => (f a -> a) -> Free f a -> a Source #

Given an applicative homomorphism from f to Identity, tear down a Free Monad using iteration.

iterM :: (Applicative f, Monad m) => (f (m a) -> m a) -> Free f a -> m a Source #

Like iter for monadic values.

Free Monads With Class

class Monad m => MonadFree (f :: Type -> Type) (m :: Type -> Type) | m -> f where Source #

Monads provide substitution (fmap) and renormalization (join):

m >>= f = join (fmap f m)

A free Monad is one that does no work during the normalization step beyond simply grafting the two monadic values together.

[] is not a free Monad (in this sense) because join [[a]] smashes the lists flat.

On the other hand, consider:

data Tree a = Bin (Tree a) (Tree a) | Tip a

instance Monad Tree where
  return = Tip
  Tip a >>= f = f a
  Bin l r >>= f = Bin (l >>= f) (r >>= f)

This Monad is the free Monad of Pair:

data Pair a = Pair a a

And we could make an instance of MonadFree for it directly:

instance MonadFree Pair Tree where
   wrap (Pair l r) = Bin l r

Or we could choose to program with Free Pair instead of Tree and thereby avoid having to define our own Monad instance.

Moreover, Control.Monad.Free.Church provides a MonadFree instance that can improve the asymptotic complexity of code that constructs free monads by effectively reassociating the use of (>>=). You may also want to take a look at the kan-extensions package (http://hackage.haskell.org/package/kan-extensions).

See Free for a more formal definition of the free Monad for a Functor.

Minimal complete definition

Nothing

Methods

wrap :: f (m a) -> m a Source #

Add a layer.

wrap (fmap f x) ≡ wrap (fmap return x) >>= f

default wrap :: forall (t :: (Type -> Type) -> Type -> Type) (n :: Type -> Type) a. (m ~ t n, MonadTrans t, MonadFree f n, Functor f) => f (m a) -> m a Source #

Instances

Instances details

Monad m => MonadFree Identity (IterT m) Source #
Instance details Defined in Control.Monad.Trans.Iter Methods wrap :: Identity (IterT m a) -> IterT m a Source #
Functor f => MonadFree f (Free f) Source #
Instance details Defined in Control.Monad.Free Methods wrap :: f (Free f a) -> Free f a Source #
Applicative f => MonadFree f (Free f) Source #
Instance details Defined in Control.Monad.Free.Ap Methods wrap :: f (Free f a) -> Free f a Source #
Functor f => MonadFree f (F f) Source #
Instance details Defined in Control.Monad.Free.Church Methods wrap :: f (F f a) -> F f a Source #
(Functor f, MonadFree f m) => MonadFree f (MaybeT m) Source #
Instance details Defined in Control.Monad.Free.Class Methods wrap :: f (MaybeT m a) -> MaybeT m a Source #
(Functor f, Monad m) => MonadFree f (FreeT f m) Source #
Instance details Defined in Control.Monad.Trans.Free Methods wrap :: f (FreeT f m a) -> FreeT f m a Source #
(Applicative f, Monad m) => MonadFree f (FreeT f m) Source #
Instance details Defined in Control.Monad.Trans.Free.Ap Methods wrap :: f (FreeT f m a) -> FreeT f m a Source #
MonadFree f (FT f m) Source #
Instance details Defined in Control.Monad.Trans.Free.Church Methods wrap :: f (FT f m a) -> FT f m a Source #
(Functor f, MonadFree f m) => MonadFree f (ExceptT e m) Source #
Instance details Defined in Control.Monad.Free.Class Methods wrap :: f (ExceptT e m a) -> ExceptT e m a Source #
(Functor f, MonadFree f m) => MonadFree f (IdentityT m) Source #
Instance details Defined in Control.Monad.Free.Class Methods wrap :: f (IdentityT m a) -> IdentityT m a Source #
(Functor f, MonadFree f m) => MonadFree f (ReaderT e m) Source #
Instance details Defined in Control.Monad.Free.Class Methods wrap :: f (ReaderT e m a) -> ReaderT e m a Source #
(Functor f, MonadFree f m) => MonadFree f (StateT s m) Source #
Instance details Defined in Control.Monad.Free.Class Methods wrap :: f (StateT s m a) -> StateT s m a Source #
(Functor f, MonadFree f m) => MonadFree f (StateT s m) Source #
Instance details Defined in Control.Monad.Free.Class Methods wrap :: f (StateT s m a) -> StateT s m a Source #
(Functor f, MonadFree f m, Monoid w) => MonadFree f (WriterT w m) Source #
Instance details Defined in Control.Monad.Free.Class Methods wrap :: f (WriterT w m a) -> WriterT w m a Source #
(Functor f, MonadFree f m, Monoid w) => MonadFree f (WriterT w m) Source #
Instance details Defined in Control.Monad.Free.Class Methods wrap :: f (WriterT w m a) -> WriterT w m a Source #
(Functor f, MonadFree f m) => MonadFree f (ContT r m) Source #
Instance details Defined in Control.Monad.Free.Class Methods wrap :: f (ContT r m a) -> ContT r m a Source #
(Functor f, MonadFree f m, Monoid w) => MonadFree f (RWST r w s m) Source #
Instance details Defined in Control.Monad.Free.Class Methods wrap :: f (RWST r w s m a) -> RWST r w s m a Source #
(Functor f, MonadFree f m, Monoid w) => MonadFree f (RWST r w s m) Source #
Instance details Defined in Control.Monad.Free.Class Methods wrap :: f (RWST r w s m a) -> RWST r w s m a Source #